They could possibly do something like that. Some other games do it to keep replays light on the data, literally record the inputs and positions of models/enemies/players. Examples of games that did this are Street Fighter 4, Dissidia FF, and Halo 3/ODST/Reach/4.

Would be pretty sweet to have in XIV, though I don't think it would happen, sadly.

Well, at least not for dungeons, trials, guildhests, and raids. PvP however, has a bigger chance of getting a feature like that. Could probably be made to work with other content.

One can hope.